Multi-mode trimming of imperfect rings
Multi-mode trimming of imperfect rings
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DOI：
10.1006/jsvi.2001.3811
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发表时间：
2001-12-06
影响因子：
4.7
通讯作者：
Fox, CHJ
中科院分区：
文献类型：
--
作者：
Rourke, AK;McWilliam, S;Fox, CHJ
本文提出了一种方法，用于修剪的固有频率的一个不完善的环，同时消除某些频率分裂。最初，被认为是一个完美的环上添加了一些不完美的质量的效果。这是通过使用瑞利-里兹方法来实现的，在该方法中，假设模态形状与完美环的模态形状相同。通过考虑逆（所谓的修剪）问题，推断出通过在环周围的特定位置处移除（最少）N个修剪质量，可以同时修剪N对模式。为了计算修剪质量位置，需要求解N个非线性代数方程。一旦实现了这一点，就可以很容易地计算出微调质量的大小。对于修整单对模式的特殊情况，可获得单个所需修整质量的大小和位置的解析解。为了修剪两对模式，它示出了一个简单的解析关系存在于两个所需的修剪质量的角位置之间，这些质量的大小可以很容易地获得。为了修剪更多的模式对，数值技术是必需的，并为此目的提出了一个数值方法。验证推导的解析结果和建议的数值计算程序是通过研究一些理论的例子。(C)北京：科学出版社.
This paper proposes a method for trimming the natural frequencies of an imperfect ring to simultaneously eliminate certain of the frequency splits present. Initially, the effect of the addition of a number of imperfection masses on a perfect ring is considered. This is achieved by using a Rayleigh-Ritz approach in which it is assumed that the mode shapes are identical to those of a perfect ring. By considering the inverse (the so-called trimming) problem it is deduced that it is possible to trim N pairs of modes simultaneously by removing (a minimum of) N trimming masses at particular locations around the ring. To calculate the trimming mass locations, it is necessary to solve N non-linear algebraic equations. Once this has been achieved, the magnitude of the trimming masses can be calculated easily. For the special case of trimming a single pair of modes, analytic solutions for the magnitude and position of the single required trimming mass are available. To trim two pairs of modes, it is shown that a simple analytic relationship exists between the angular positions of the two required trimming masses and that the magnitude of these masses can be obtained easily. To trim more pairs of modes, numerical techniques are required and for this purpose a numerical procedure is proposed. Validation of the derived analytic results and the proposed numerical procedure is achieved by studying a number of theoretical examples. (C) 2001 Academic Press.